He is believed to have driven to the airport and gone to the international terminal, before pulling out the weapon and slashing travellers.
Three men were left with cuts and scrapes after the attack at San Francisco International Airport on Friday evening local time, according to police.
They were treated for minor injuries and were able to continue with their travels, officials said.
A man has been arrested in connection with the attack. Police have not yet released details about his identity or motives.
Airport duty manager Russell Mackey told local media it was still unclear whether the attacker was a passenger himself.